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4 votes
Enter the number that belongs in

the green box.
6.78
[?]°
10
4
29°
Round to the nearest hundredth.

Enter the number that belongs in the green box. 6.78 [?]° 10 4 29° Round to the nearest-example-1
User Afroditi
by
8.2k points

1 Answer

4 votes

Answer:

Number that belongs in the green box (rounded to the nearest hundredth) = 16.62

Explanation:

Finding the angle using the Law of Sines:

  • Because we don't know whether this is a right triangle, we can use the Law of Sines to find the measure of the angle (let's call it A).
  • This Law can be used to calculate an unknown angle in a non-right triangle when two sides and one angle opposite on of the sides is known.

The Law of Sines works through proportions between the sines of a triangle's angles and the sides opposite these angles:

a / sin A = b / sin B = c / sin C

Thus, we can substitute 6.78 for b, the 29° angle for B, and 4 for a in the Law of Sines to find A, the measure of the unknown angle to the nearest hundredth:

(4 / sin A = 6.78 / sin 29) * sin A

(4 = (6.78 / sin 29) * sin A) / 6.78 / sin 29

4 / (6.78 / sin 29) = sin A

sin^-1 (4 / (6.78 / sin 29)) = A

16.62003032 = A

16.62 = A

Thus, the measure of the unknown angle is about 16.62°.

User Boyan Bozhidarov
by
8.4k points

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